Relational lattices are obtained by interpreting lattice connectives as natural join and inner union between database relations. Our study of their equational theory reveals that the variety generated by relational lattices has not been discussed in the existing literature. Furthermore, we show that addition of just the header constant to the lattice signature leads to undecidability of the qua...

Nominal sets were introduced by Gabbay and Pitts (Gabbay and Pitts, 1999). This paper describes a step towards universal algebra over nominal sets. There has been some work in this direction, most notably by M.J. Gabbay (Gabbay, 2008). The originality of our approach is that we do not start from the analogy between sets and nominal sets. As shown in (Gabbay, 2008), this is possible, but it requ...

In the category of Hom-Leibniz algebras we introduce the notion of Hom-corepresentation as adequate coefficients to construct the chain complex from which we compute the Leibniz homology of Hom-Leibniz algebras. We study universal central extensions of Hom-Leibniz algebras and generalize some classical results, nevertheless it is necessary to introduce new notions of α-central extension, univer...

To any cleft Hopf Galois object, i.e., any algebra H obtained from a Hopf algebra H by twisting its multiplication with a two-cocycle α, we attach two “universal algebras” AH and U α H . The algebra A α H is obtained by twisting the multiplication of H with the most general two-cocycle σ formally cohomologous to α. The cocycle σ takes values in the field of rational functions on H. By construct...

We show that the central charge $k$ reduction of universal extension elliptic Hall algebra is isomorphic to trace, or zeroth Hochschild homology, quantum Heisenberg category $k$. As an application, we construct large families representations algebra.

We consider the universal central extension of the Lie algebra Vect(S 1)⋉C ∞ (S 1). The coadjoint representation of this Lie algebra has a natural geometric interpretation by matrix analogues of the Sturm-Liouville operators. This approach leads to new Lie superalgebras generalizing the well-known Neveu-Schwartz algebra.

We show that when a co-involutive Hopf C *-algebra S coacts via δ on a C *-algebra A, there exists a full crossed product A × δ S, with universal properties analogous to those of full crossed products by locally compact groups. The dual Hopf C *-algebra is then defined byˆS := C × id S.

We continue the study of twisted automorphisms of Hopf algebras started in [4]. In this paper we concentrate on the group algebra case. We describe the group of twisted automorphisms of the group algebra of a group of order coprime to 6. The description turns out to be very similar to the one for the universal enveloping algebra given in [4].

We introduce and study bimeasurings from pairs of bialge-bras to algebras. It is shown that the universal bimeasuring bialgebra construction, which arises from Sweedler's universal measuring coalgebra construction and generalizes the finite dual, gives rise to a contravariant functor on the category of bialgebras adjoint to itself. An interpretation of bimeasurings as algebras in the category o...

We use order zero maps to express the Jiang-Su algebra Z as a universal C∗-algebra on countably many generators and relations, and we show that a natural deformation of these relations yields the stably projectionless algebra W studied by Kishimoto, Kumjian and others. Our presentation is entirely explicit and involves only ∗-polynomial and order relations.